Scenario: In a classroom, there are 30 students. 20 students play football, 15 students play basketball, and 10 students play both sports. What is the probability that a randomly selected student plays either football or basketball?
Question
Scenario: In a classroom, there are 30 students. 20 students play football, 15 students play basketball, and 10 students play both sports. What is the probability that a randomly selected student plays either football or basketball?
Solution
To solve this problem, we first need to understand how many students play either football or basketball.
Step 1: Identify the total number of students who play football or basketball. This is the sum of the students who play football and the students who play basketball.
20 (football players) + 15 (basketball players) = 35
Step 2: However, we have double-counted the students who play both sports. We need to subtract the number of students who play both sports from the total we calculated in step 1.
35 - 10 (students who play both) = 25
So, there are 25 students who play either football or basketball.
Step 3: Now, we need to calculate the probability. The probability is the number of students who play either football or basketball divided by the total number of students.
25 (students who play either sport) / 30 (total students) = 0.8333
So, the probability that a randomly selected student plays either football or basketball is 0.8333 or 83.33% when expressed as a percentage.
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